A system for withdrawing body fluid is known from DE 100 26 172 A1 in which a deformable double cone is used as a compression unit to increase the inner pressure in a region of the pressed body part. In this process the downward pressure is partially converted into a movement in a secondary direction with a component at right angles to the primary direction until the upper and lower cone region rest against one another. In this state the constriction which ties off the body part is located above the plate-like support member whereas the puncture or blood removal site still lies within the collapsed double cone. This requires a point access for blood withdrawal with the risk that excess blood can contaminate the device. Moreover, the body part can accidentally slip if the coefficient of friction between the compression unit and the skin falls below a lower limit for example due to skin sweat or fat deposits. In this case a malfunction can also occur if the compression unit completely folds through into the inside of the device.